Sami Abed

University of Diyala · topology

In this article we consider general properties of Michelson contrast (visibility) and provide generalization of Michelson contrast for positive operators of countably decomposable W *-algebras.

In this article we propose two measures one that gives an answer "How far is an element from central" and the other "How far a linear functionalis from tracial?" As we see from the article the measure of centrality incase of positive bounded operators has a tight connection with the conceptof invertibility.

Let P, Q be projections on a Hilbert space. We prove the equivalence of the following conditions: (i) PQ + QP ≤ 2(QPQ)p for some number 0 < p ≤ 1; (ii) PQ is paranormal; (iii) PQ is M*-paranormal; (iv) PQ = QP. This allows us to obtain the commutativity criterion for a von Neumann algebra. For a positive normal functional φ on von Neumann algebra \...

We propose the conditions for a continuous function to be projection-convex, i.e. f(λp+ (1 − λ)q) ≤ λf(p) + (1 − λ)f(q) for any projections p and q and any real λ ∈ (0, 1). Also we obtain the characterization of projections commutativity and the characterization of trace in terms of equalities for non-flat functions.

For a normed algebra A and natural numbers k we introduce and investigate the ∥ · ∥ closed classes Pk (A). We show that P1(A) is a subset of Pk (A) for all k. If T in P1(A), then Tn lies in P1(A) for all natural n. If A is unital, U, V ∈ A are such that ∥U∥ = ∥V∥ = 1, VU = I and T lies in Pk (A), then UTV lies in Pk (A) for all natural k. Let A be...